The Improvement And Application Of MCMC Based On Wavelet Transform

Multivariate stochastic volatility(MSV)model is a volatility model based on stochastic process theory to describe the time-varying characteristics related to the financial volatility spillovers.Moreover,due to the introduction of random error term,it is identical with the actual results compared with the generalized autoregressive conditional heteroscedasticity(GARCH)model,and has less impact on financial data.MSV model is sensitive to financial data fluctuation,and proved to be more suitable for time series modeling.However,because MSV model contains a large number of unmeasurable potential variables,it is unable to measure its real likelihood function.As a result,there exist lots of restrictions imposed on model parameters estimation.Consequently,accurate estimation results are difficult to be derived from foregone approaches.During the previous academic researches,scholars generally adapt Markov Chain Monte Carlo(MCMC)method,aiming at the estimation focused on MSV.MCMC method is mainly to solve the problem of random number generated by computer.Its essence is to combine simulation sampling and dynamic iteration to generate a pseudorandom integral.Its advantage is that the parameter estimation of real likelihood function keep impervious from high dimension data.The program is simple and easy to debug.Therefore,many researchers combine MCMC algorithm with parameter estimation of multivariate stochastic volatility model to expand the application space of financial econometric modeling.However,with the continuous expansion of the scope of high-frequency data analysis,the financial time series measured by hours,minutes and seconds gradually appear,and the drawbacks in convergence speed and time consumption with the original MCMC method do as well.Therefore,it is necessary to propose an efficient method for MSV model estimation.Recently,wavelet theory and multi-resolution analysis development makes it possible to improve MCMC algorithm.Wavelet transform originates within Fourier theory,which is able to extract information from basic data through the transform in different dimensions effectively.We analyzed the signal in detail by using operation functions,and the original signal is filtered by using orthogonal high-pass and low-pass filters to realize state space transformation,aiming at effectively diminishing the model autocorrelation and refining on MCMC.The MCMC computational results are significantly related to the time-varying characteristics and processing requirements of financial time series.With information technology development,the parallel sampling theory can effectively solve the problem that MCMC method is inefficient when the dimension of MSV model becomes higher.It can directly optimize the sampling process of the algorithm through simple programming.The advantage of parallel sampling mechanism is independently adaptive to MCMC proposal distribution,and different parallel sampling mechanisms are adopted for the parameters to be estimated with different initial distributions,so as to improve the computational efficiency of MCMC algorithm for parameter estimation of multivariate random fluctuation model.According to the previous research results,this paper improves the traditional MCMC algorithm,and focuses on an improved MCMC method for parameter estimation of multivariate random fluctuation model,that is,the parallel MCMC method with wavelet transform.The MCMC method decomposes and reconstructs all levels of signals based on the threshold function,and reduces the autocorrelation and spatial complexity of the model through wavelet filtering.For the parameters to be estimated with different prior distributions in MSV model,the improved MCMC algorithm adopts the parallel scheme of Gibbs sampling,optimizes the sampling and iterative operation process of the algorithm,which can theoretically maximize the simulation iteration advantages of MCMC algorithm and greatly promote the operation speed.To empirically test the parallel MCMC estimation result,this paper selects the weekly closing price data of WTI and Brent from July 10,2006 to April 23,2020,and selects Daubechies wavelet basis function to analyze the original signal.We filtered the noise and keep the real information.The multivariate random fluctuation model is established according to the de-noising reconstructed signal.To a certain extent,the traditional method and the improved methd are used for MSV model estimation,and the convergence,significance,fitting effect,running time and operation precision of the empirical results are concerned.The practical effect of parallel MCMC algorithm based on wavelet transform is tested from five aspects of degree.The empirical outcomes demonstrate that as for GC-MSV,DC-MSV and DGC-t-MSV during the short period,the convergence results of the improved algorithm and the traditional algorithm are not significantly different in accuracy and accuracy,and the model fitting degree is high.However,the running time of simulated annealing and iterative estimation of the parallel MCMC algorithm based on Wavelet transform is greatly reduced,and its acceleration ratio is several times of the traditional algorithm,which is suitable for the application.It is used to estimate the MSV parameters of financial time series in high dimension data.